Weather refers to the more local changes in the climate we see around us, on short timescales from minutes to hours to days to weeks. Examples are familiar – rain, snow, clouds, winds, thunderstorms, heat waves and floods.
Climate refers to longer-term averages (they may be regional or global), and can be thought of as the weather averaged over several seasons, years or decades. Climate change is harder for us to get a sense of because the timescales involved are much longer, and the impact of climate changes can be less immediate. Examples of climate change include several drier-than-normal summers, a trend of, say, winters becoming milder from our grandparents’ childhood to our own, or variations in effects like El Niño or La Niña.